Import Question JSON

Current Question (ID: 21392)

Question:

$\text{The resistivity of a } 0.8 \text{ M solution of an electrolyte is } 5 \times 10^{-3} \, \Omega \, \text{cm. If } \lambda_m = 2.5 \times 10^x,$ $\text{the value of } x \text{ is:}$

Options:

1. $4$
2. $8$
3. $5$
4. $9$

Solution:

$k = \frac{10^3}{5} \, S \, \text{cm}^{-1}$ $\lambda_m = \kappa X \frac{1000}{m} = \frac{\frac{10^3}{5} \times 1000}{0.8} = \frac{200 \times 10^3}{0.8}$ $= \frac{2 \times 10^5}{0.8} = 2.5 \times 10^5$ $x = 5$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}